3D trigonometry

3D Trigonometry in year 10 is one of those subjects that lots of kids have issues with. Students traditionally learn just one topic at a time, are tested and then move to the next topic. With 3D trigonometry are all of a sudden faced with using lots of maths all at once.

Topics that all come together:

• Parallel lines (in 3D)
• Alternate/Complementary/Supplementary etc angles
• Polygon properties
• Trigonometric ratios
• Pythagoras' theorem
• Sine Rule
• Cosine Rule
• Oblique and isometric drawing
• 3d visualisation
• Volume, Surface area
• Algebra (in all its guises)

My students have seen some success in this topic through the use of "wireframes" (made of skewers and connected with a hot glue gun) and templates placed in the wireframes to indicate various right angled and non right angled triangles. It also helps them see parallel lines and equivalent lengths/angles. This seems to be the concrete element they need to put all the other stuff in place.

I also try to introduce the topic multiple times throughout the year as new concepts are introduced (eg. parallel lines - > volume -> pythagoras -> trig ratios -> sine rule -> cosine rule)

Also useful is the discussion on solving triangles here.